In apparatus known hitherto, the selecting member is formed by a needle which sticks into the heald stack directly after the frontmost heald of the stack and then displaces the frontmost heald in the longitudinal direction (that is, in the feed direction) of the heald stack to the drawing-in position. The healds used are either provided with a taper at their narrow edges at the selecting point or they must have a so-called keyhole. This means that healds without tapered narrowed edges or a keyhole could not hitherto be drawn in automatically in such apparatus.